Problem: Simplify the following expression: $ z = \dfrac{-1}{10} - \dfrac{7p - 1}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{-1}{10} \times \dfrac{3}{3} = \dfrac{-3}{30} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{7p - 1}{3} \times \dfrac{10}{10} = \dfrac{70p - 10}{30} $ Therefore $ z = \dfrac{-3}{30} - \dfrac{70p - 10}{30} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-3 - (70p - 10) }{30} $ Distribute the negative sign: $z = \dfrac{-3 - 70p + 10}{30}$ $z = \dfrac{-70p + 7}{30}$